Journal
NATURE COMMUNICATIONS
Volume 10, Issue -, Pages -Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/s41467-019-10841-6
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Funding
- ERC [FPTOpt-277998]
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For many stochastic processes, the probability S(t) of not-having reached a target in unbounded space up to time t follows a slow algebraic decay at long times, S(t) similar to S-0/t(theta). This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent theta has been studied at length, the prefactor S-0, which is quantitatively essential, remains poorly characterized, especially for non-Markovian processes. Here we derive explicit expressions for S-0 for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for S-0 are in good agreement with numerical simulations, even for strongly correlated processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.
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